Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778645 | Advances in Mathematics | 2017 | 28 Pages |
Abstract
A subshift on a group G is a closed, G-invariant subset of AG, for some finite set A. It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of “forbidden patterns”, to be strongly aperiodic if all point stabilizers are trivial, and weakly aperiodic if all point stabilizers are infinite index in G. We show that groups with at least 2 ends have a strongly aperiodic SFT, and that having such an SFT is a QI invariant for finitely presented groups. We show that a finitely presented torsion free group with no weakly aperiodic SFT must be QI-rigid. The domino problem on G asks whether the SFT specified by a given set of forbidden patterns is empty. We show that decidability of the domino problem is a QI invariant.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
David Bruce Cohen,